Bell and Greenberger, Horne, and Zeilinger theorems revisited

Ryff, Luiz Carlos

doi:10.1119/1.18758

Cited by 18 publications

(13 citation statements)

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“…Simply setting ⟨α⟩ exp = ⟨α⟩ LHV T = M −2 and inverting expression (14), we obtain ⟨ a 2 ⟩ nonlocal > 1 2. This verifies the already-proved limit of 50% fidelity, which is necessary for violation of any Bell-type inequality based on the GHZ theorem [40,41]. In most cases it is also the bound for discriminating less than maximally entangled states.…”

Section: Comparison Of Different Methodssupporting

confidence: 78%

Practical and efficient experimental characterization of multiqubit stabilizer states

et al. 2015

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Vast developments in quantum technology have enabled the preparation of quantum states with more than a dozen entangled qubits. The full characterization of such systems demands distinct constructions depending on their specific type and the purpose of their use. Here we present a method that scales linearly with the number of qubits, for characterizing stabilizer states. Our approach allows simultaneous extraction of information about the fidelity, the entanglement and the nonlocality of the state and thus is of high practical relevance. We demonstrate the efficient applicability of our method by performing an experimental characterization of a photonic four-qubit cluster state and three-and four-qubit Greenberger-Horne-Zeilinger states. Our scheme can be directly extended to larger-scale quantum information tasks.

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Section: Comparison Of Different Methodssupporting

confidence: 78%

Practical and efficient experimental characterization of multiqubit stabilizer states

et al. 2015

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“…According to the data shown in Fig. 2, the fidelity observed for the state prepared in our experiment is (79.6 ± 0.5)%, which is greatly exceed the minimum bound of 50%31. Thus, with high statistical significance, genuine n-qubit entanglement of the GHZ states created in our experiment is confirmed.…”

Section: Discussionsupporting

confidence: 62%

Extreme violation of local realism with a hyper-entangled four-photon-eight-qubit Greenberger-Horne-Zelinger state

Cao

Zhao

et al. 2014

Sci Rep

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The highest qubit Ardehali inequality violation with 203 standard deviations is first experimentally demonstrated using the hyper-entangled four-photon-eight-qubit Greenberger-Horne-Zeilinger (GHZ) state. Moreover, we experimentally investigate the robustness of the Ardehali inequality for the four-, six-, and eight-qubit GHZ states in a rotary noisy environment systematically. Our results first validate the Ardehali' theoretical statement of relation between violation of Ardehali inequality and particle number, and proved that Ardehali inequality is more robust against noise in larger number qubit GHZ states, and provided an experimental benchmark for us to estimate the safety of quantum channel in the noisy environment.

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“…This novel situation attracted again attention to the original Bell inequality [26]. We also point to related theoretical studies on the original Bell inequality which were done during the previous years, see [27,28,29,30,31]. In [29,31], it is, for example, shown that, unlike the CHSH inequality, the original Bell inequality distinguishes between classicality and quantum separability.…”

Section: Introductionmentioning

confidence: 84%

Evaluating the Maximal Violation of the Original Bell Inequality by Two-Qudit States Exhibiting Perfect Correlations/Anticorrelations

Khrennikov

Loubenets

2018

Entropy

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We introduce the general class of symmetric two-qubit states guaranteeing the perfect correlation or anticorrelation of Alice and Bob outcomes whenever some spin observable is measured at both sites. We prove that, for all states from this class, the maximal violation of the original Bell inequality is upper bounded by 3 2 and specify the two-qubit states where this quantum upper bound is attained. The case of two-qutrit states is more complicated.Here, for all two-qutrit states, we obtain the same upper bound 3 2 for violation of the original Bell inequality under Alice and Bob spin measurements, but we have not yet been able to show that this quantum upper bound is the least one. We discuss experimental consequences of our mathematical study.

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Bell and Greenberger, Horne, and Zeilinger theorems revisited

Cited by 18 publications

References 0 publications

Practical and efficient experimental characterization of multiqubit stabilizer states

Practical and efficient experimental characterization of multiqubit stabilizer states

Extreme violation of local realism with a hyper-entangled four-photon-eight-qubit Greenberger-Horne-Zelinger state

Evaluating the Maximal Violation of the Original Bell Inequality by Two-Qudit States Exhibiting Perfect Correlations/Anticorrelations

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